On 15/02/2013 06:56, John Doty wrote:
>> hard to debug programming language (assembler).
>
> There are always bugs in non-trivial software.
>
> There are always layers of misunderstanding:
>
> 1. The engineers (hardware and software) never fully understand the application, and are usually too stubborn to admit this.
>
> 2. The programmers never fully understand the hardware, and are usually too stubborn to admit this.
>
> 3. The operators never fully understand the machine, and are usually too stubborn to admit this.
>
> Hardware is not perfectly reliable, especially in radiology departments where there's much EMI and possibly other problems like stray neutrons (I know from experience that unhardened microcontrollers misbehave near the MGH cyclotron in Boston, even in "shielded" areas). Operators are often distracted, tired, and pressured. And misspelling of silly made-up words is common, too ;-)
>
> One must therefore assume that if the hardware can be put into a fatal configuration, it will be at some point. When it actually happens, the retrospective details of how it happened are misleading. The fundamental engineering issue is that one must design so that the ordinary, routine failures do not cascade to fatality. By removing the hardware interlock, the Therac engineers had designed the system to fail.
>
>
I would really like to endorse that. I feel that some people like to
scoff at software developers and their supposedly inadequate methods
without proposing a viable alternative. For example, program proving
seems an impossible dream for serious programs, and would in any case
require a formal specification that might itself contain bugs.
All the most complex artifacts we have are either software, or contain
large amounts of software. Software engineers are routinely required to
deliver a level of complexity unheard of say 50 years ago - yet some
people like to scoff when they sometimes fail.
Anything that is extremely complex is susceptible to mistakes -
particularly if it can't really be tested until it is finished. Take for
example, the Mars probe that crashed because of a mixup over physical
units. Clearly such a trivial mistake would be unthinkable in a simpler
project - I presume it got overlooked because it was hidden among vast
amounts of other detail.
Anyone using Mathematica (or any other software) for a serious task has
to take responsibility for the results he/she uses, and even then, there
are still some risks involved. So for a very trivial example if you
decide to check:
In[6]:= Integrate[Exp[ax]x,x]
Out[6]= (E^ax x^2)/2
by doing:
In[7]:= D[%,x]
Out[7]= E^ax x
Your check will return the original expression, and maybe lead you to
believe you have the answer you wanted! Maybe if you recognise that you
are prone to make that type of mistake, you should examine anything
important in FullForm - but ultimately the user has to be responsible.
David Bailey
http://www.dbaileyconsultancy.co.uk